arXiv subjects
Publications and source records attributed to Heinrich Saller.
Let a quantum network be a Fermi-Dirac assembly of Fermi-Dirac assemblies of ...of quantum points, interpreted topologically. The simplest quantum-network vacuum modes with exact conservation of relativistic energy-momentum and angular momentum also support the local non-Abelian groups of the standard model, torsion and gravity. The spacetime points of these models naturally obey parastatistics. We construct a left-handed vacuum network among others.
Seeking a relativistic quantum infrastructure for gauge physics, we analyze spacetime into three levels of quantum aggregation analogous to atoms, bonds and crystals. Quantum spacetime points with no extension make up more complex link units with microscopic extension, which make up networks with macroscopic extension. Such a multilevel quantum theory implies parastatistics for the lowest level entities without additional physical assumptions. Any hypercubical vacuum mode with off-diagonal long-range order that is covariant under $\POINCARE$ also has bonus internal symmetries somewhat like those of the standard model. A vacuum made with the dipole link proposed earlier has too much symmetry. A quadrupole link solves this problem.
The numerical input for the quantitative consequences of the electroweak standard model, the hypercharge and isospin coupling constants and the Higgs field ground state mass value, are interpreted as normalizations of the symmetries involved. Using an additional statistical argument, a first order quantitative determination of the Weinberg angle as a normalization ratio gives the experimentally acceptable value $\tan^2þ={1\over3}$.
The discrete symmetries of the Lorentz group are on the one hand a `complex' interplay between linear and anti-linear operations on spinor fields and on the other hand simple linear reflections of the Minkowski space. We define operations for T, CP and CPT leading to both kinds of actions. These operations extend the action of SL(2,C), representing the action of the proper orthochronous Lorentz group SO^+(1,3) on the Weyl spinors, to an action of the full group O(1,3). But it is more instructive to reverse the arguments. The action of O(1,3) is the natural way how SL(2,C) together with its conjugation structure acts on Minkowski space. Focusing on the symmetries of these (anti-)linear operations we can for example distinguish between CP-invariant and CP-violating symmetries. This is important if gauge symmetries are included. It turns out that, contrary to the general belief, CP and T are not compatible with SU(n) for n > 2, especially with colour-SU(3) or with the U(3)-Cabibbo-Kobayashi-Maskawa matrix.
I discuss the indefinite metrical structure of the time-space translations as realized in the indefinite inner products for relativistic quantum fields, familiar in the example of quantum gauge fields. The arising indefinite unitary nondiagonalizable representations of the translations suggest as the positive unitarity condition for the probability interpretable positive definite asymptotic particle state space the requirement of a vanishing nilpotent part in the time-space translations realization. A trivial Becchi-Rouet-Stora charge (classical gauge invariance) for the asymptotics in quantum gauge theories can be interpreted as one special case of this general principle - the asymptotic projection to the eigenstates of the time-space translations.